Question

Solve without using calculator. Use two decimal places. \[\sqrt{200} - \sqrt{32}\]

Answer 1

please just show how

Answer 2

sqrt(200) = 10sqrt(2)
and sqrt(32) = 4sqrt(2)
sqrt(2) = 1.414 approx.. easy now?

Answer 3

Okay, step by step, factor both the terms.

Answer 4

how did you get the approximation?

Answer 5

sqrt(2x100) - sqrt (2x16) = 10sqrt2 - 4sqrt2 = 6sqrt2

Answer 6

well yeah i get \[6\sqrt2\] but how to solve that?

Answer 7

Now factor \(\sqrt 32\)

Answer 8

i just want to know the value of \(6\sqrt 2\) without calculator use -_-

Answer 9

I always remember sqrt2 = 1.4something, not sure about this one

Answer 10

\(\Large \color{purple}{\rightarrow \sqrt{32} = 4\sqrt{2} }\)

Answer 11

lol not good enough

Answer 12

how could i verify it is 1.4

Answer 13

\(\Large \color{purple}{\rightarrow 6\sqrt{2} - 4\sqrt{2} = 2\sqrt{2} }\)

Answer 14

Are you taking calculus? you could use a linear approximation to get it if you know how

Answer 15

yeah...that...i need to know the formula for linear approx

Answer 16

You can find square roots using division method.

Answer 17

and how to use it

Answer 18

http://www.homeschoolmath.net/teaching/square-root-algorithm.php

Answer 19

See the long division method.

Answer 20

idk what you're talking about @ParthKohli o.O

Answer 21

I definitely didn't learn that method, and guess and check sucks. not sure what to tell you

Answer 22

Man!

Answer 23

The division method is what I am talking about.

Answer 24

http://www.kwiznet.com/p/takeQuiz.php?ChapterID=11046&CurriculumID=48&Num=2.53

Answer 25

nevermind then haha

Answer 26

seems no one knows linear approximation

Answer 27

see between which square numbers 2 lies.
it lies between 1 and 4
see to which number 2 is closer.
it is closer to 1 than 4.
nw
sqrt of 1 is 1
sqrt of 4 is 2
so sqrt of 2 must be closer to 1
square 1.1, 1.2, 1.3, 1.4 and see whose square is approximately 2 . then that is the sqrt of 2. hope that helps.

Answer 28

well to find x^1/2 ,,you can use calculus,,let f(x) = x^1/2
take a no. close to 2 whose sqrt is known to you
let x=1.96 (as sqrt(1.96) =1.4) { you can also take 2.25 as sqrt(2.25) = 1.5}
dx = 2 - 1.96 = 0.04
now according to lebinitz rules,, dy = f(x+dx) - f(x)
thus dy = 2^1/2 - 1.96^1/2
also,,dy = (f'(x))dx
thus dy = 1/(2x^1/2) (dx) = 1/(2*1.4) ( 0.04) = 0.04/2.8 = 1/70
substitute it in 1st eqn
thus 2^1/2 = 1/70 + 1.4 = 1.414 ....
hope it was helpful..

Answer 29

note that above approx could be made as x>>dx ..